A216982 Anti-Chowla's function: sum of anti-divisors of n except the largest.

0, 0, 0, 0, 2, 0, 5, 3, 2, 7, 5, 5, 10, 7, 8, 3, 17, 16, 5, 11, 8, 21, 19, 7, 22, 7, 24, 27, 5, 16, 21, 37, 26, 7, 29, 8, 25, 45, 26, 28, 14, 38, 27, 11, 56, 27, 29, 24, 39, 47, 8, 59, 53, 16, 37, 19, 36, 57, 51, 67, 16, 37, 70, 3, 41, 42, 87, 67, 8, 55

Offset: 1

Author

Juri-Stepan Gerasimov, Feb 19 2013

Keywords

• nonn

Comments

Numbers n such that Chowla's function(n) = a(n): 1, 2, 3, 10, 15, 28, 75, 88, 231, 284, 602,...

Places n where a(n) is zero: 1, 2, 3, 4, 6, 96,...

Fixed points of this sequence: 17, 53, 127, 217, 385, 2321,...

Places n where a(n) equals the largest anti-divisor: 1, 2, 7, 10, 31, 37, 39, 55, 78, 160, 482, 937, 1599, 2496,...

Numbers n such that n -/+ 1 and a(n -/+ 1) are all primes: 6, 18, 72, 102, 108, 198, 270, 432, 570, 882,...

Examples

			Anti-divisors of 7 are 2, 3, 5, so a(7) = 2 + 3 = 5.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A048050, A066272, A066417, A066481, A130799, A218767.

Programs

Maple

A216982 := proc(n)
        A066417(n)-A066481(n) ;
end proc: # R. J. Mathar, Feb 23 2013

PARI

a(n)=if(n<5,0,my(k=valuation(n, 2)); sigma(2*n+1)+sigma(2*n-1)+sigma(n>>k)<<(k+1)-2-20*n\/3) \\ Charles R Greathouse IV, Mar 05 2013

Formula

a(n) = A066417(n) - A066481(n).